Question

Each box holds 48 pencils. The chart below shows the number of pencils in 1 box and 5 boxes.

Answer 1

Using a proportional relationship, we have that:

• The table is completed as follows: x = 4, y = 192; x = 6, y = 288; x = 9; y = 432;

• 6 boxes are not enough for 300 pencils, 7 are needed.

What is a direct proportional relationship?

A direct proportional relationship is a function in which the output variable is found with the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

From the table in this problem, the constant is given as follows:

k = 240/5 = 48/1 = 48.

Hence the relationship is:

y = 48x.

Then:

• When x = 4, y = 48(4) = 192.

• When x = 6, y = 48(6) = 288.

• When x = 9, y = 48(9) = 432.

For 300 pencils, the number of boxes is given by:

48x = 300

x = 300/48

x = 6.25.

There are not decimal parts of a box, a complete box is needed, hence 7 boxes are needed, meaning that 6 boxes are not enough for 300 pencils.

More can be learned about proportional relationships at brainly.com/question/10424180

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